Chapter 8, Problem 78CR

a.

To determine

To find: the probability that the person selected is a person who does not favor the proposal.

Answer to Problem 78CR

The probability that the person selected is a person who does not favor the proposal is 0.416.

Explanation of Solution

Given information: A sample of 400 college students, 75 faculty members, and 25

administrators were asked whether they favored a proposed increase in the annual activity fee to enhance student life on campus. Of the students, 237 favor and 163 oppose the proposal. Of the faculty, 37 favor and 38 oppose the proposal. Of the administrators, 18 favor and 7 oppose the proposal. A person is selected at random from the sample.

Formula used.

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Calculation:

Total number of student = 400.

Student in favor is = 237.

Student in oppose is =163.

Total number of faculty = 75.

Faculty in favor is = 37.

Faculty in oppose is =38.

Total number of administrators = 25.

Administrators in favor is = 18.

Administrators in oppose is =7.

The sample space is the total number of people =400+75+25=500.

n(S) = 500.

Total number of people who does not favor the proposal=163+38+7=208,

n(E) =208

The probability that the person selected is a person who does not favor the proposal:

  $P(E)=\frac{n(E)}{n(S)}=\frac{208}{500}=0.416$ .

b.

To determine

To find: the probability that the person selected is a student who favor the proposal.

Answer to Problem 78CR

The probability that the person selected is a student who favor the proposal is 0.474.

Explanation of Solution

Given information: A sample of 400 college students, 75 faculty members, and 25

administrators were asked whether they favored a proposed increase in the annual activity fee to enhance student life on campus. Of the students, 237 favor and 163 oppose the proposal. Of the faculty, 37 favor and 38 oppose the proposal. Of the administrators, 18 favor and 7 oppose the proposal. A person is selected at random from the sample.

Formula used.

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Calculation:

Total number of student = 400.

Student in favor is = 237.

Student in oppose is =163.

Total number of faculty = 75.

Faculty in favor is = 37.

Faculty in oppose is =38.

Total number of administrators = 25.

Administrators in favor is = 18.

Administrators in oppose is =7.

The sample space is the total number of people =400+75+25=500.

n(S) = 500.

Total number of student who favor the proposal=237,

n(E) =237

The probability that the person selected is a student who favor the proposal:

  $P(E)=\frac{n(E)}{n(S)}=\frac{237}{500}=0.474$ .

c.

To determine

To find: the probability that the person selected is a faculty who favor the proposal.

Answer to Problem 78CR

The probability that the person selected is a faculty who favor the proposal is 0.074.

Explanation of Solution

Given information: A sample of 400 college students, 75 faculty members, and 25

administrators were asked whether they favored a proposed increase in the annual activity fee to enhance student life on campus. Of the students, 237 favor and 163 oppose the proposal. Of the faculty, 37 favor and 38 oppose the proposal. Of the administrators, 18 favor and 7 oppose the proposal. A person is selected at random from the sample.

Formula used.

If an event has n(E) equally likely outcomes and its sample space S has n(S) equally likely outcomes, then the probability of event is given by,

  $P(E)=\frac{n(E)}{n(S)}.$

Calculation:

Total number of student = 400.

Student in favor is = 237.

Student in oppose is =163.

Total number of faculty = 75.

Faculty in favor is = 37.

Faculty in oppose is =38.

Total number of administrators = 25.

Administrators in favor is = 18.

Administrators in oppose is =7.

The sample space is the total number of people =400+75+25=500.

n(S) = 500.

Total number of faculty who favor the proposal=37,

n(E) =237

The probability that the person selected is a faculty who favor the proposal:

  $P(E)=\frac{n(E)}{n(S)}=\frac{27}{500}=\mathrm{0.074.}$ .